BN.com Gift Guide

Norm Inequalities for Derivatives and Differences / Edition 1

Paperback (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $29.11
Usually ships in 1-2 business days
(Save 27%)
Other sellers (Paperback)
  • All (6) from $29.11   
  • New (4) from $29.11   
  • Used (2) from $55.01   

Overview

Norm inequalities relating (i) a function and two of its derivatives and (ii) a sequence and two of its differences are studied. Detailed elementary proofs of basic inequalities are given. These are accessible to anyone with a background of advanced calculus and a rudimentary knowledge of the Lp and lp spaces.
The classical inequalities associated with the names of
Landau, Hadamard, Hardy and Littlewood, Kolmogorov,
Schoenberg and Caravetta, etc., are discussed, as well as their discrete analogues and weighted versions. Best constants and the existence and nature of extremals are studied and many open questions raised. An extensive list of references is provided, including some of the vast Soviet literature on this subject.

Read More Show Less

Product Details

  • ISBN-13: 9783540563877
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 3/5/1993
  • Series: Lecture Notes in Mathematics Series , #1536
  • Edition description: 1992
  • Edition number: 1
  • Pages: 152
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.34 (d)

Table of Contents

Introduction 1
1 Unit Weight Functions 3
1.1 The Norms of y and y[superscript (n)] 3
1.2 The Norms of y, y[superscript (k)], and y[superscript (n)] 6
1.3 Inequalities of Product Form 12
1.4 Growth at Infinity 26
2 The Norms of y, y', y'' 35
2.2 The [actual symbol not reproducible] Case 35
2.3 The L[superscript 2] Case 36
2.4 Equivalent Bounded Interval Problems for R 38
2.5 Equivalent Bounded Interval Problems for R[superscript +] 43
2.6 The L[superscript 1] Case 45
2.7 Upper and Lower Bounds for k(p, R) and k(p, R[superscript +]) 47
2.8 Extremals 55
2.9 Continuity as a Function of p 77
2.10 Landau's Inequality for Nondifferentiable Functions 80
3 Weights 84
3.1 Inequalities of the Sum Form 84
3.2 Inequalities of Product Form 95
3.3 Monotone Weight Functions 97
3.4 Positive Weight Functions 104
3.5 Weights with Zeros 109
4 The Difference Operator 117
4.1 The Discrete Product Inequality 117
4.2 The Second Order Case 120
4.3 Extremals 123
References 144
Subject Index 149
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)